A Transport Equation Approach to Green Functions and Self-force Calculations

TL;DR

This paper introduces a transport equation approach for calculating Green functions in curved spacetime, enhancing the matched expansions method for self-force computations and broadening applications in quantum field theory and gravity.

Contribution

It presents a novel transport equation method for Green function calculation within the matched expansions framework, applicable to self-force, radiation reaction, and quantum gravity problems.

Findings

Effective transport equation methods for Green functions in quasilocal regions

Application of matched expansions to self-force calculations

Relevance to quantum field theory and quantum gravity

Abstract

In a recent work, we presented the first application of the Poisson-Wiseman-Anderson method of `matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function which are respectively valid in the `quasilocal' and `distant past' regimes, and which may be matched together within the normal neighbourhood. In this article, we introduce the method of matched expansions and discuss transport equation methods for the calculation of the Green function in the quasilocal region. These methods allow the Green function to be evaluated throughout the normal neighborhood and are also relevant to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity.